[Jump to code hierarchy]

Self-dual code over \(R\)

Description

An additive linear code \(C\) over a ring \(R\) that is equal to its dual, \(C^\perp = C\), where the dual is defined with respect to some inner product.

Member of code lists

Primary Hierarchy

Classical Domain
Ring Kingdom
Ring codeECC
\(R\)-linear codeECC
Dual code over \(R\)
Parents
Dual code over \(R\)
Self-dual code over \(R\)
Children
Self-dual additive codeSelf-dual linear
Octacode
The octacode is self-dual over \(\mathbb{Z}_4\).
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)— see instructions

edit on this site

Zoo Code ID: self_dual_over_rings

Cite as:
“Self-dual code over \(R\)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/self_dual_over_rings
BibTeX:
@incollection{eczoo_self_dual_over_rings, title={Self-dual code over \(R\)}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/self_dual_over_rings} }
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/self_dual_over_rings

Cite as:

“Self-dual code over \(R\)”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/self_dual_over_rings

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/rings/dual/self_dual_over_rings.yml.